Problem: Multiply and simplify the following complex numbers: $({4-2i}) \cdot ({-5+4i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({4-2i}) \cdot ({-5+4i}) = $ $ ({4} \cdot {-5}) + ({4} \cdot {4i}) + ({-2i} \cdot {-5}) + ({-2i} \cdot {4i}) $ Then simplify the terms: $ (-20) + (16i) + (10i) + (-8i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (16 + 10)i - 8 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -20 + (16 + 10)i - (-8) $ The result is simplified: $ (-20 + 8) + (26i) = -12+26i $